An apparatus and a method for filtering sectioning wastes of a microtome that are present in an air stream is suggested. The apparatus encompasses an aspiration device. With the aspiration device, sectioning waste can be aspirated from a blade region of the microtome with an air stream. The aspiration device comprises a main filter in which the sectioning wastes can be filtered from the air. In order to allow inadvertently aspirated histological sections to be retrieved again without mix-up, the apparatus according to the present invention has an aspiration device comprising a prefilter that is arranged between the blade region and the main filter and prefilters the sectioning wastes. The present invention further relates to a microtome.